Which Team Won?

This is a straightforward problem that does not necessarily require any sophisticated analysis. Students are given the data from a team running race with 10 runners in each of the three teams. They are asked to design one or more methods of deciding the winning team and to compare results. The underlying theme is that of using a mathematical model appropriate to the practical task but noting that being ‘fair’ is not a precise concept.

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Summary

This is a straightforward problem that does not necessarily require any sophisticated analysis. Students are given the data from a team running race with 10 runners in each of the three teams. They are asked to design one or more methods of deciding the winning team and to compare results. The underlying theme is that of using a mathematical model appropriate to the practical task but noting that being ‘fair’ is not a precise concept.

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Mathematical strand

Statistics

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Prior knowledge

Appreciation of basic handling of data is required.

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Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson / Edexcel

•OCR

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Suggested approaches

Suitable for group or paired work, with plenty of opportunity for collaboration and discussion with the whole class on what is the best method of determining the winning team.

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Resources/documentation

In addition to these teacher notes/guidance there are:  Teacher notes  Handout with relevant data and questions posed

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Relevant digital technologies

This would be very appropriate for using a spreadsheet approach.

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Possible extensions

Whilst the problem does not require a sophisticated approach, it could be a way of introducing weighted means and for research into the variety of models used in practice for determining the winning team in a variety of sporting contexts or indeed other contexts (for example, in the Eurovision song contest, etc.).

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Acknowledgement

This is based on a resource originally developed by Derek Robinson (Bishop Luffa School, Chichester) and modified for the CMSP by David Burghes (CIMT, Plymouth University).